Reduce to lowest terms: $ \dfrac{4}{3} \div - \dfrac{7}{6} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{6}$ is $- \dfrac{6}{7}$ Therefore: $ \dfrac{4}{3} \div - \dfrac{7}{6} = \dfrac{4}{3} \times - \dfrac{6}{7} $ $ \phantom{ \dfrac{4}{3} \times - \dfrac{6}{7}} = \dfrac{4 \times -6}{3 \times 7} $ $ \phantom{ \dfrac{4}{3} \times - \dfrac{6}{7}} = \dfrac{-24}{21} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-24}{21} = \dfrac{-24 \div 3}{21 \div 3} = -\dfrac{8}{7} $